%------------------------------------------------------------------------------
% File : hopCoP---0.1
% Problem : SET618+3 : TPTP v9.0.0. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/execute.py 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n019.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri Jul 25 03:32:23 PM UTC 2025
% Result : Theorem 0.12s 0.35s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 4
% Syntax : Number of formulae : 14 ( 14 unt; 0 def)
% Number of atoms : 14 ( 13 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 3 ( 3 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 3 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 10 ( 0 sgn 6 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(prove_th93,plain,
! [B] : symmetric_difference(B,B) = empty_set,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_th93) ).
fof(prove_th93_negated,plain,
~ ! [B] : symmetric_difference(B,B) = empty_set,
inference(negate_conjecture,[status(cth)],[prove_th93]) ).
cnf(21,plain,
symmetric_difference(sK4,sK4) != empty_set,
inference(cnf,[status(esa)],[prove_th93_negated]) ).
cnf(l0,plain,
symmetric_difference(sK4,sK4) != empty_set,
inference(instantiation,[status(thm)],[21]) ).
fof(symmetric_difference_defn,plain,
! [B,C] : symmetric_difference(B,C) = union(difference(B,C),difference(C,B)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',symmetric_difference_defn) ).
cnf(0,plain,
symmetric_difference(X0,X1) = union(difference(X0,X1),difference(X1,X0)),
inference(cnf,[status(esa)],[symmetric_difference_defn]) ).
cnf(l3,plain,
symmetric_difference(sK4,sK4) = union(difference(sK4,sK4),difference(sK4,sK4)),
inference(instantiation,[status(thm)],[0]) ).
fof(idempotency_of_union,plain,
! [B] : union(B,B) = B,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',idempotency_of_union) ).
cnf(1,plain,
union(X0,X0) = X0,
inference(cnf,[status(esa)],[idempotency_of_union]) ).
cnf(l12,plain,
union(difference(sK4,sK4),difference(sK4,sK4)) = difference(sK4,sK4),
inference(instantiation,[status(thm)],[1]) ).
fof(self_difference_is_empty_set,plain,
! [B] : difference(B,B) = empty_set,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',self_difference_is_empty_set) ).
cnf(2,plain,
difference(X0,X0) = empty_set,
inference(cnf,[status(esa)],[self_difference_is_empty_set]) ).
cnf(l11,plain,
difference(sK4,sK4) = empty_set,
inference(instantiation,[status(thm)],[2]) ).
cnf(final,plain,
$false,
inference(ground_refutation,[status(thm)],[l0,l3,l12,l11]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SET618+3 : TPTP v9.0.0. Released v2.2.0.
% 0.11/0.12 % Command : /export/starexec/sandbox2/solver/bin/execute.py 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.12/0.33 % Computer : n019.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Mon Jul 21 22:08:19 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.12/0.34 % launching worker at depth: 1
% 0.12/0.34 % launching worker at depth: 2
% 0.12/0.34 % launching worker at depth: 4
% 0.12/0.34 % launching worker at depth: 3
% 0.12/0.34 % launching worker at depth: 8
% 0.12/0.34 % launching worker at depth: 5
% 0.12/0.34 % launching worker at depth: 6
% 0.12/0.34 % launching worker at depth: 7
% 0.12/0.34 % launching worker at depth: 9
% 0.12/0.34 % launching worker at depth: 10
% 0.12/0.35 % SZS status Theorem for theBenchmark
% 0.12/0.35 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------